Mode statistics in random lasers

Representing an ensemble of random lasers with an ensemble of random matrices, we compute the average number of lasing modes and its fluctuations. The regimes of weak and strong coupling of the passive resonator to the environment are considered. In the latter case, contrary to an earlier claim in the literature, we do not find a power-law dependence of the average mode number on the pump strength. For the relative fluctuations, however, a power law can be established. It is shown that, due to the mode competition, the distribution of the number of excited modes over an ensemble of lasers is not binomial.